Solve clearly

2. An oil rich economy owns 100 barrels of oil which can be extracted at a unit cost of $2 a barrel. It faces a demand curve Q(t)=100-2P(t), t=1,2,3 years. The discount rate is 12%. Assume that the world will end at the end of the third year. a. How much oil will be extracted in each of the three periods if a social planner was making decisions? b. How much oil would be extracted if the planner was a monopolist? c. Now consider the fact that the Minister of Energy is optimistic about the future and believes that the economy can harness the abundant solar energy it gets, instead of oil. This new backstop energy will be available in unlimited quantities at the beginning of the third year at a price of $34 per barrel of oil equivalent. What would the price of oil be in the three periods? Does supply equal demand in the third period? Explain